In this paper we propose audio encryption algorithm based on standard circle map. The proposed scheme contains bit level sample permutation using pseudorandom generator. Provided cryptanalysis includes number of tests demonstrating the security of proposed encryption algorithm

Bonchev, Lachezar

Kordov, Krasimir

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Mathematical and Software Engineering, Vol 3, No 2 (2017), 183–189Varεpsilon Ltd, varepsilon.comUsing Circle Map for Audio EncryptionAlgorithmKrasimir Kordov and Lachezar BonchevDepartment of Computer Informatics, Faculty of Mathematics andInformatics, Konstantin Preslavski University of Shumen, 9712 Shumen,BulgariaAbstractIn this paper we propose audio encryption algorithm based on standard circle map.The proposed scheme contains bit level sample permutation using pseudorandom gen-erator. Provided cryptanalysis includes number of tests demonstrating the security ofproposed encryption algorithm.Subject Codes: 68P25, 94A60Keywords: encryption, audio encryption, wav encryption, encryption algorithm1 IntroductionDigital data encryption is a process for securing stored and transmitted data. According tothe specific type of data, encryption algorithm are designed to work in specific way.In recent years multimedia files are often preferred as data carries in social networks,communications and Internet as general. Such files are audio files, video files and digitalimages. Therefore our focus is on multimedia files and more concrete on audio files. Securingaudio files for safe storing and transmission requires designing of new encryption algorithms.Most common approach for modeling encryption algorithms is bit level symmetric en-cryption using preudorandom generators(PRG) [8, 9, 11]. Pseudorandom bit generators arebased on complex discrete mathematics or chaos based [5, 13, 14] but simple for program-ming realization. Their goal is to produce unlimited sequence of random bits therefor theycan be used as building units for cryptographic [12] and steganographic [15, 16] algorithms.Audio encryption algorithms require strong level of security therefor they are subject ofdetailed cryptanalysis. Various experiments can be performed for determining resistance ofproposed algorithm to attacks, defining their level of security [3, 7].1832 Pseudorandom Bit Generator Based on Two CircleMaps and XOR Function2.1 Circle Map DescriptionThe Circle map [2] maps points on the circle back onto a circle. The Circle map is a nonlineariterated map calculated byθn+1 = (θn +Ω−K2pisin(2piθn)) mod 1, (1)where Ω is a constant that is the fixed angular progression of the sinusoidal oscillator,and K is the coupling strength.2.2 Bit generation schemeIn our previous work we proposed a pseudorandom bit generator based on two circle mapsand XOR function [4]. The proposed scheme is based on the following two Circle mapequations:θ1,m+1 = (θ1,m +Ω1 −K12pisin(2piθ1,m)) mod 1θ2,n+1 = (θ2,n +Ω2 −K22pisin(2piθ2,n)) mod 1,(2)where θ1,m, Ω1, K1, θ2,n, Ω2 and K2 are the initial conditions. The new generator consistsof the following steps:Step 1: The initial values θ1,m, Ω1, K1, θ2,n, Ω2 and K2 of the two Circle maps fromEq. (2) are determined.Step 2: The two chaotic maps from Eq. (2) are iterated for L1 and L2 times, respectively.Step 3: The iteration of the Eq. (2) continues, and as a result, two real fractions θ1,iand θ2,j , are generated and post-processed as follows:s1,i = mod(integer(θ1,i × 109)), 2)s2,j = mod(integer(θ2,j × 109)), 2),where integer(x) returns the integer part of x, truncating the value at the decimalpoint, and mod(x, y) returns the reminder after division.Step 4: Perform XOR operation between s1,i and s2,j to get a single output bit.Step 5: Return to Step 3 until the bit stream limit is reached.Used initial values are: θ1,m = 0.5, θ2,n = −0.25, Ω1 = Ω2 = 0.7128281828459045,K1 = K2 = 0.5, L1 = L2 = 200.Statistical tests were made for determining the necessary cryptographic security of the pro-posed generator in [4] and similar scheme can be found in [6, 10].Key space includes all the initial values indicating the key space is more than 2179 [4]providing sufficient security against brute-force key search attacks [1].1843 Audio Encryption SchemeIn this section we present audio encryption algorithm using the pseudorandom generatordescribed in 2.2. Produced random bits are extracted for sample permutation of audio files.Sample permutation is realized by using simple XOR function.3.1 Encryption and Decryption AlgorithmAudio encryption algorithm consists of the following steps:Step 1: Header bits from plain audio file A are transfered into file A′ without crypto-graphic modifications.Step 2: The bits in the sample are encrypted using XOR operation with the sameamount of bits prodused by the pseudorandom generator from 2.2.Step 3: Encrypted sample from Step 2 is transfered into file A′Step 4: Repeat Steps 2-3 until end of plain file A is reached.Step 5: The produced output file A′ is the final encrypted audio file.The proposed audio encryption method is implemented in programing language C++.Keeping the header bits in both plain and encrypted audio files allows us to perform furthercryptanalysis tests by comparing the samples values of both files.Decryption algorithm is the same as encryption scheme because the proposed cryptographicalgorithm is symmetric using the same steps and the same key for audio decryption.4 Cryptographic AnalysisThe cryptanalysis determines the reliability of encryption algorithms. In this section weprovide the results of empirical tests performed using proposed audio encryption algorithmin 3.1.4.1 Waveform PlottingWaveform plotting represents the amplitude of audio signal distributed in time. Figure 1shows wave amplitude of plain audio file 1(a) and wave amplitude of the same file, afterencryption 1(b).Simple visual analysis can determine that the two waves shown in 1 are completelydifferent, indicating the good properties of the proposed audio encryption algorithm.4.2 Correlation AnalysisMeasuring correlation between samples values of plain and encrypted files is standard methodfor evaluating cryptographic algorithms. Calculating correlation coefficient determines thelevel of correlation between two files.Correlation coefficient can be calculated as follows:rxy =cov(x, y)√D(x)√D(y), (3)185(a) Plain audio file(b) Encrypted audio fileFigure 1: Waveform of Plain audio file 1(a) and corresponding Encrypted audio file 1(b)whereD(x) =1NN∑i=1(xi − x)2,D(y) =1NN∑i=1(yi − y)2,cov(x, y) =N∑i=1(xi − x)(yi − y),N is the number of samples processed from audio file (plain or encrypted), xi and yi arevalues of corresponding samples of both files, x and y are mean values of samples for eachfile, and finally cov(x, y) is covariance between both files.Table 1 shows some of the obtained result values from our tests. Experiments were madewith different file size.Plain Encrypted File Bytes in CorrelationAudio File Audio File Size Sample CoefficientSample1.wav encSample1.wav 100kb 2 -0.020451Sample2.wav encSample2.wav 150kb 2 0.049001Sample3.wav encSample3.wav 500kb 2 -0.013219Sample4.wav encSample4.wav 1MB 2 -0.018381Sample5.wav encSample5.wav 5MB 2 0.006555Table 1: Correlation Between Plain and Encrypted Audio FilesResults in Table 1 indicates that all values are close to zero which means there is nodependence between the two files. This demonstrates the good cryptographic properties ofthe proposed audio encryption algorithm.1864.3 Key Sensitivity AnalysisThe secure encryption algorithms require strong resistance to secret key attacks. The fol-lowing key sensitivity analysis provides encryption and decryption experiment using verysimilar secret keys. K1 is the secret key used for encryption and it contains all the initialvalues of the parameters and variables for PRG in 2.2. Very similar secret key K2 is usedfor decryption of the encrypted file. K2 is obtained by slightly changing a single variablefrom K1 and keeping all the other variables unchanged. θ2,n for K1 is -0.25 and for K2 is-0.26.(a) Plain audio file(b) Encrypted audio file with K1(c) Decrypted audio file with K2Figure 2: Waveform of Plain audio file 2(a), encrypted file using K1 2(b) and Decrypted fileusing K2 2(c)Figure 2 demonstrates unsuccessful attempt for decryption using very similar secret key.This indicates highly key sensitivity of the proposed audio encryption algorithm, provingresistibility against secret key attacks.4.4 Speed Test PerformanceThe encryption time of cryptographic algorithms is important aspect for their evaluation.We have tested the encryption time for variety of files with different size to determine the al-gorithm encryption time. Testing computer configuration was 2.40 GHz Intel R© CoreTM i7-3630QM Dell Inspiron laptop. Part of the results are shown in the following Table 2The results from Table 2 determine encryption speed ≈ 0.45 mb/sec which indicates fasttime performance of the proposed audio encryption algorithm.187File File Bytes in EncryptionName Size Sample TimeSample1.wav 100kb 2 0.202sSample2.wav 150kb 2 0.320sSample3.wav 500kb 2 1.246sSample4.wav 1MB 2 2.230sSample5.wav 5MB 2 12.728sTable 2: Speed Test Performance5 ConclusionNew model of audio encryption is presented in this paper. The audio encryption algorithmis modeled by using preudorandom bit generator based on two circle maps. The proposedmethod permutates data in samples with bit level operation XOR using actual data insample and binary sequence produced by pseudorandom generator.Security analysis is provided by waveform plotting of plain and encrypted files, correlationcoefficient is calculated for plain and encryption files, key sensitivity is tested, and speed testperformance is measured. The obtained results demonstrate good cryptographic propertiesof the proposed audio encryption algorithm. Considering the results, we can conclude thatthe proposed algorithm is resistant to cryptographic attacks and can be used for audioencryption.AcknowledgementThis work is partially supported by the Scientific research fund of Konstantin PreslavskiUniversity of Shumen under the grant No. RD-08-124/06.02.2017.References[1] Alvarez, G., Li, S., Some Basic Cryptographic Requirements for Chaos-Based Cryptosys-tems, International Journal of Bifurcation and Chaos, 16 (2006), 2129–2151.[2] Essl, G., Circle Maps as a Simple Oscillators for Complex Behavior: I. Basics, in ICMC,2006, pp. 356359.[3] Hato, E., Shihab, D., Lorenz and Rossler Chaotic System for Speech Signal Encryption,International Journal of Computer Applications, Vol 128, 2015, no. 11, 09758887.[4] Kordov, K., Modified pseudo-random bit generation scheme based on two circle mapsand XOR function, Applied Mathematical Sciences, Vol. 9, 2015, no. 3, 129-135, http://dx.doi.org/10.12988/ams.2015.411887.[5] Kordov, K., Signature Attractor Based Pseudorandom Generation Algorithm, AdvancedStudies in Theoretical Physics Vol. 9, 2015, no. 6, pp. 287-293, http://dx.doi.org/10.12988/astp.2015.517[6] Malchev, D., Ibryam, I., Construction of Pseudorandom Binary Sequences Using ChaoticMaps, Applied Mathematical Sciences, Vol. 9, 2015, no. 78, 3847-3853, http://dx.doi.org/10.12988/ams.2015.52149.[7] Sheu, L. J.,A speech encryption using fractional chaotic systems, Nonlinear Dynamics,Vol. 65 2011, no.1, 103-108.188[8] Stoyanov, B.P., Chaotic cryptographic scheme and its randomness evaluation, in 4thAMiTaNS’12, AIP Conference Proceedings, 1487, 397–404, 2012, http://dx.doi.org/10.1063/1.4758983.[9] Stoyanov, B.P., Pseudo-random bit generator based on Chebyshev map, in 5th AMi-TaNS’13, AIP Conference Proceedings, 1561 (2013), 369–372, http://dx.doi.org/10.1063/1.4827248.[10] Stoyanov, B.P., Using Circle Map in Pseudorandom Bit Generation, in 6th AMiTaNS14,AIP CP 1629 (2014), 460 - 463, http://dx.doi.org/10.1063/1.4902309.[11] Stoyanov, B., Pseudo-random Bit Generation Algorithm Based on Chebyshev Polyno-mial and Tinkerbell Map, Applied Mathematical Sciences, Vol. 8, 2014, no. 125, 6205–6210, http://dx.doi.org/10.12988/ams.2014.48676.[12] Stoyanov, B., Kordov, K. Image encryption using Chebyshev map and rotation equation,Entropy vol. 17 (2015), no.4, 2117-2139.[13] Stoyanov, B., Kordov, K., Novel Zaslavsky Map Based Pseudorandom Bit GenerationScheme, Applied Mathematical Sciences, Vol. 8, 2014, no. 178, 8883-8887, http://dx.doi.org/10.12988/ams.2014.410879.[14] Stoyanov, B., Kordov, K., Pseudorandom Bit Generator with Parallel Implementation,In Large-Scale Scientific Computing 2014, Lecture Notes in Computer Science, vol. 8353,pp. 557-564, ISSN: 0302-9743[15] Zhelezov S., Modified Algorithm for Steganalysis, Mathematical and Software Engineer-ing, Vol. 1, No. 2 (2015), 31-36. ISSN 2367-7449[16] Zhelezov, S., Paraskevov, H., Possibilities for steganographic parallel processing witha cluster system, Contemporary Engineering Sciences, Volume 8, Issue 20, 2015,ISSN:1313-6569Copyright c© 2017 Krasimir Kordov and Lachezar Bonchev. This is an open access article distributedunder the Creative Commons Attribution License, which permits unrestricted use, distribution, and repro-duction in any medium, provided the original work is properly cited.189

Using Circle Map for Audio Encryption Algorithm

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Using Circle Map for Audio Encryption Algorithm

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